Problem $3[16$ pts$]$: A simple, ideal Diesel cycle has a compression ratio of $18$ and a cut off ratio of $1\mathrm{.}6.$ The inlet conditions are $280$ K and $100$ kPa $.$ The engine is a $4$stroke engine, and has a displacement of $3\mathrm{.}2$ L $.$ Use the cold air standard assumptions for this problem.

a$)$ Find the temperature at all four steps of the cycle

b$)$ Find the mass specific heat input to the cycle

c$)$ Find the mass specific work outputs during the heat addition step, and the expansion step $[$ANSWER FOR STEP $2$:$153\mathrm{.}26k\frac{J}{k}g]$

d$)$ Find the thermal efficiency of the cycle $[$ANSWER: $65\mathrm{.}1\%]$

e$)$ Find the power output of the cycle at a speed of $2500$ rpm